Frame assembly and dither drive for a coriolis rate sensor

ABSTRACT

An apparatus for producing signals indicative of both a Coriolis rate and an acceleration along a preferred axis while decoupling extraneous vibration and motion that would introduce errors into the signals, and a driving mechanism for vibrating the apparatus at a dither frequency. The apparatus includes a parallelogram frame (50) including two accelerometer support surfaces (24, 26) on which are mounted two accelerometers (20 and 22) having their sensitive axes in parallel alignment. The accelerometer support surfaces are connected to opposite ends of a flex member (52), which includes six flexures (32, 34, 36, 38, 40, 42) having parallel bending axes. Two of the flexures (34, 38) are disposed at opposite ends of one side of each flexure member, and have a &#34;long&#34; axis that is substantially parallel to the sensitive axes of the accelerometers and aligned with a line connecting their centers of percussion. The centers of mass of the accelerometers and their associated supporting surfaces are coincident with the centers of percussion, and are rigidly connected by the two flexures and by one side (30) of each flex member. This solid metal path between the centers of percussion minimizes common mode errors. A driving mechanism (64) is connected to the parallelogram frame and is opertive to drive the accelerometers at a desired frequency, causing them to vibrate back and forth in a direction substantially transverse to their sensitive axes. The driving mechanism includes a mounting plate (72) and a coil frame (66) on which are mounted two electromagnetic coils (70) having a &#34;C&#34; shaped core (80). The driving mechanism is mounted so that the core faces a pole piece (84) attached to the parallelogram frame and its moment of inertia is trimmed to equal that of the parallelogram frame. It is connected to the parallelogram by a link (88) and provides a reactionless driving force.

TECHNICAL FIELD

This invention generally pertains to a Coriolis rate sensor, and moreparticularly, to a parallelogram frame used in such a sensor and a drivemechanism for vibrating the parallelogram frame.

BACKGROUND INFORMATION

Angular rate of rotation about a given coordinate axis may be measuredby moving (e.g., vibrating) an accelerometer along an axis normal to theaccelerometer's sensitive axis and normal to the rate axis about whichrotation is to be measured. For example, consider a set of X, Y, Zcoordinate axes fixed in a body whose rotation rate is to be measured,and an accelerometer also fixed in the body with its sensitive axisaligned along the Z axis. If the angular rotation vector of the bodyincludes a component along the X axis, then periodic motion of theaccelerometer along the Y axis will result in a periodic Coriolisacceleration acting in the Z direction that will be sensed by theaccelerometer. The magnitude of the Coriolis acceleration isproportional to the velocity along the Y axis and the rotation rateabout the X axis. As a result, the output of the accelerometer includesa DC or slowly changing component that represents the linearacceleration of the body along the Z axis, and a periodic component thatrepresents the rotation of the body about the X axis. The accelerometeroutput can be processed, along with the outputs of accelerometers thathave their sensitive axes in the X and Y directions and that are movedalong the Z and X axes, respectively, to yield linear acceleration andangular rate about the X, Y and Z axes. Such signal processing isdescribed in U.S. Pat. Nos. 4,445,376 and 4,590,801.

As described in U.S. Pat. No. 4,590,801, one preferred embodiment of arotation rate sensor comprises, for each axis, two accelerometersoriented with their sensitive axes parallel or antiparallel to oneanother, and means for dithering (i.e., vibrating) the accelerometersalong an axis normal to their sensitive axes. A suitable method formounting such accelerometer pairs is described in U.S. Pat. No.4,510,802. A side view of a structure shown in FIG. 3 of that patentillustrates a mount for two accelerometers centered on mounting surfacesat the top and at the bottom of a parallelogram frame. The side of theparallelogram frame shown in the figure includes six pivots, comprisingthin metal flexures aligned with their bending axes in parallel, one ofthe flexures being disposed at each of the four corners and at thecenters of the vertical sides of the parallelogram frame.

Prior designs for rotation rate sensors like the one briefly describedabove have been subject to problems associated with dynamic imbalance ofthe parallelogram structure, and the sensitivity of the structure tovibration occurring in a direction other than parallel to the axis alongwhich they are dithered. For example, if the parallelogram frame justdescribed is subjected to a vibration along an axis parallel with thesensitive axes of the accelerometers, both accelerometers shouldexperience a common mode force, and produce an equal, though opposite,output that cancels in the angular rate channel. However, due to thetransverse (i.e., cross axis) flexibility of the thin metal flexures andof the supporting surfaces on which the accelerometers are mounted, thesame vibrational movement is not applied to the two accelerometers. Anystructural resonance in the frame may exacerbate this problem. As aresult, the output signal produced by the rate sensor includes an errorin the angular rate channel that is proportional to the difference inthe nominal common mode vibration to which the accelerometers aresubjected.

The prior art driving mechanism used to provide the dither motion orvibration along an axis transverse to the sensitive axes of theaccelerometers is typically disposed adjacent one side of theparallelogram frame. Due to an inequality of mass distribution (ormoment of inertia) between the driving mechanism and the parallelogramframe, the parallelogram frame may experience an imbalanced torque whenboth the frame and driving mechanism are subjected to a vibrationdirected parallel to the accelerometer sensitive axes. In additiondifferences in the moment of inertia of the driving mechanism and theparallelogram frame may cause a variation in the driving force appliedto the frame, when it is subjected to an angular vibration about itsrotation sensitive axis. Either of these two effects may result in asubstantial error in the angular rate channel signal.

SUMMARY OF THE INVENTION

The present invention is directed to a Coriolis rate sensor apparatus inwhich extraneous motion or vibration that might tend to introduce errorsin the output signal produced by the rate sensor is either decoupled orcanceled. A further aspect of the invention is directed to a drivingmechanism for vibrating the Coriolis rate sensor frame.

A Coriolis rate sensor constructed according to the present inventionincludes a parallelogram frame having two accelerometer support surfacesattached to opposite ends of a flex member. The flex member includes sixflexures having parallel bending axes. Two of the flexures that aredisposed at opposite ends of one side of the flexure member have a crossaxis that is substantially parallel to the accelerometer supportsurfaces.

An accelerometer is mounted on each of the accelerometer supportsurfaces, having a preferred axis for sensing acceleration that isaligned with one of the two flexures. In addition, each of theaccelerometers is disposed so that its center of percussion is rigidlyconnected to the center of percussion of the other accelerometer by thetwo flexures and the one side of the flex member.

Driving means are disposed adjacent the parallelogram frame and areoperative to drive the accelerometers at a desired frequency, causingthe accelerometers to vibrate back and forth in a directionsubstantially transverse to their preferred axes as the parallelogramframe pivots at each flexure. The driving means and the parallelogramframe possess certain characteristics which tend to decouple or cancelextraneous motion. For example, the moment of inertia of the drivingmeans is made equal to the combined moment of inertia of theparallelogram frame and the accelerometers. In addition, the center ofgravity associated with each accelerometer support surface and theaccelerometer mounted thereon is coincident with the center ofpercussion of that accelerometer and the centers of gravity are rigidlyconnected to each other by the aligned flexures and by one side of theflex member in the same manner as the centers of percussion.

The parallelogram frame includes a base plate disposed generally at itscenter. A cross bar that extends from one side of the flex member to theother side connects to the base plate and is adapted to connect to thesupporting structure. Each end of the cross bar is connected to a sideof the flex member by one of the flexures. The moment of one side of theflex member about the bending axis of the flexure connecting the crossbar to that side equals the moment of the other side of the flex memberabout the bending axis of the flexure connecting the cross bar to theother side. Thus, the parallelogram frame is not subjected to arotational torque due to a vibrational component directed parallel tothe preferred axes of the accelerometers. In addition, the parallelogramframe is substantially symmetrical in both shape and mass about acentral plane defined by the center of the base plate that extendsthrough the frame intermediate both accelerometers and transverse totheir preferred axes. Therefore, the parallelogram frame is notsubjected to a rotational torque due to any vibrational componentdirected transversely to the preferred axes of the accelerometers andparallel to the bending axes of the flexures.

The parallelogram frame is also substantially symmetrical in both shapeand mass about a plane that extends through the centers of percussion ofthe accelerometers, and transverse to the bending axes of the flexures.Consequently, the frame is dynamically balanced with respect to the backand forth vibration that is provided by the driving means. A solid linkconnects the driving means and the parallelogram frame. Consequently,any angular vibration about the rotation sensitive axis acting on one ofthe parallelogram frame and the driving means also must act on the otherthrough the link.

The parallelogram frame further includes a plurality of tuning strapsdisposed adjacent one side of the flex member. The tuning straps connectthe accelerometer support surfaces to the base plate and are selected tohave a stiffness which just balances the stiffness of the flexures. As aresult, noncommon mode tilting rotations resulting from cross axiscompliance of the flexures are eliminated, and the accelerometers aresubjected only to a tilting rotation about their centers of percussion.

The drive mechanism for the Coriolis rate sensor includes a supportplate having means for attaching the support plate to a supportingstructure in a position adjacent the Coriolis rate sensor. A coil frameis provided in which is mounted an electromagnetic coil. The coil frameis connected to the support plate along a flexure having a bending axisabout which the coil frame may pivotally deflect. On the electromagneticcoil is disposed a core face that is proximate to and facing toward acorresponding pole face of a pole piece mounted on the Coriolis ratesensor. When a power supply is connected to energize the electromagneticcoil, the core face and its corresponding pole face are attracted towardeach other.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram conceptually illustrating a parallelogram frameassembly in which two accelerometers are mounted and are vibrated alongan axis transverse to their preferred (i.e., sensitive) axes;

FIG. 2 is an isometric view showing a parallelogram frame for a Coriolisrate sensor and a driving mechanism for vibrating the parallelogramframe, wherein the driving mechanism has been separated from its normalmounting position adjacent the frame;

FIG. 3 is a side elevational view of a Coriolis rate sensor including aparallelogram frame and a driving mechanism in accordance with thepresent invention;

FIG. 4 is a top plan view of the Coriolis rate sensor shown in FIG. 3;

FIG. 5 is an end elevational view of the Coriolis rate sensor of FIGS. 3and 4;

FIG. 6 is a cross sectional view taken along section line 6--6 of FIG.4, illustrating the internal assembly of the Coriolis rate sensor;

FIG. 7 is an isometric cut-away view of the driving mechanism comprisingthe present invention;

FIG. 8 is an isometric view of a base plate used in the parallelogramframe;

FIG. 9 is a graphic representation of a simplified model illustratingthe use of tuning straps to off-set a spring stiffness associated withflexures used in the parallelogram frame;

FIG. 10 is a graphic side view of an electromagnet core and a pole pieceused in the driving mechanism showing in an exaggerated fashion thebevel applied to the core face and the pole face to maintain the centerof force between the two in a constant position as the two faces tilttoward each other;

FIG. 11 shows the graphic illustration of the core face and pole face ofFIG. 10, when the two are tilted toward each other; and

FIG. 12 illustrates a portion of a flexure in an isometric viewidentifying the three orthogonal axes associated with the flexure.

DISCLOSURE OF THE PREFERRED EMBODIMENTS

FIG. 1 schematically illustrates a parallelogram arrangement forvibrating accelerometers 20 and 22 along the Y axis. The accelerometersare mounted with their sensitive axes substantially parallel to the Zaxis and anti-parallel to one another, the sensitive axis ofaccelerometer 20 being directed in a positive direction along the Z axisand the sensitive axis of accelerometer 22 being directed in a negativedirection along the Z axis. Accelerometers 20 and 22 are secured toaccelerometer support members 24 and 26, respectively, which in turn areconnected to a pair of linkage members 28 and 30 by pivots 32 through38. Linkage members 28 and 30 are mounted at central pivots 40 and 42,respectively. Support members 24 and 26 are both parallel to the Y axis.When linkage members 28 and 30 are vibrated about central pivots 40 and42, respectively, through angles ±θ, accelerometers 20 and 22 willvibrate along the Y axis with an amplitude approximately equal to ±R θwhere R represents the length of the linkage arm 28 or 30 measured fromone of the central pivots 40 or 42 to one of the other pivots 32 through38. In FIG. 1, the angle ψ represents an initial offset (with respect tothe Z axis) about which such vibration occurs.

When a sinusoidal drive force is applied to the arrangement shown inFIG. 1, the accelerations along the Y and Z axes resulting from themotion of the accelerometers are as follows:

    A.sub.y =ω.sup.2 Rθcosψsinωt         (1)

A_(z) =ω² Rθsin ψsinωt+ω² Rθ² cosψcos2ωt (2)

where ω represents the angular frequency of vibration through angle θ.In equations (1) and (2) above, it is assumed that the driving force isproportional to sinωt, i.e., that the drive force is zero at time zero.The acceleration along the Z axis (A_(z)) of accelerometers 20 and 22due to vibration by the mechanism illustrated in FIG. 1 is relativelysmall for small values of θ and ψ, and will essentially cancel out whenthe signal output from the accelerometers is processed. The motion ofaccelerometers 20 and 22 is therefore essentially linear along the Yaxis for small angles of θ and ψ. The angular amplitude θ preferably hasa value of 0.01 through 0.1 radians, and ψ preferably has a value ofless than 0.01 radians. Suitable values for the frequency ω are in therange of 200 through 1000 radians per second. Angular rotation Ω_(x)about the X axis (the rotation sensitive axis) produces a Coriolis forcehaving an acceleration A_(z) defined by equation (2).

A preferred embodiment of an apparatus for implementing the vibratingparallelogram motion depicted graphically in FIG. 1 and a drivingmechanism for driving the apparatus so that accelerometers mounted onthe apparatus are vibrated back and forth, transverse to their sensitiveaxes, are shown in FIGS. 2 through 8. Initially, attention is directedto FIG. 3 wherein a side elevational view of a preferred embodiment ofthe invention is shown. Reference numeral 50 generally denotes aparallelogram frame including two accelerometer support surfaces 24 and26 on which are respectively mounted accelerometers 20 and 22 (not shownin this Figure). Parallelogram frame 50 is preferably machined from astainless steel having good flexural fatigue limit characteristics. Justas was graphically illustrated in FIG. 1, the parallelogram frame 50shown in FIG. 3 includes four pivots at each of its four corners,defining a parallelogram comprising a flex member 52. The pivots areimplemented in the preferred embodiment using thin circular arc metalflexures 32 through 38, each having three orthogonal axes. (For purposesof defining these axes, a representative portion of flexure 32 is shownin FIG. 12, wherein are identified a bending axis 47, a cross axis 48,and a longitudinal or "long" axis 49). Turning back to FIG. 3, flexmember 52 further includes linking members 28 and 30 that extend betweenaccelerometer support members 24 and 26. The centers of linking members28 and 30 are connected by flexures 40 and 42 to a cross bar mountingtab 54. Cross bar mounting tab 54 extends outwardly from the generallyplanar surface of flex member 52 and includes a mounting hole 56 throughwhich a bolt may be inserted to secure the parallelogram frame 50 to asupporting structure (not shown). The supporting structure wouldtypically be a part of an object that is subject to angular motion andlinear acceleration that the Coriolis rate sensor is intended tomeasure.

Each of flexures 32 through 42 includes a characteristic bending axis asdefined above, which is transverse to the planar surface of flex member52; however, the "long" axes of flexures 34 and 38 are oriented at 90°to the "long" axes of the other flexures, lying within a plane 58 thatextends through the centers of percussion of both accelerometers 20 and22, parallel to the bending axes of the flexures. Furthermore,accelerometers 20 and 22 are mounted on accelerometer support surfaces24 and 26 so that within plane 58, the center of gravity of the combinedmass of accelerometer 20, support surface 24, and associatedcounterweight 44 and electronic package 21 is coincident with the centerof percussion of accelerometer 20, and the center of gravity of thecombined mass of accelerometer 22, support surface 26, and theassociated counterweight 44 and electronic package 25 is coincident withthe center of percussion of accelerometer 22. The significance of theorientation and alignment of flexures 34 and 38 relative to the centersof percussion of the accelerometers and the centers of gravity of theaccelerometers and their support surfaces will be discussed furtherhereinbelow.

Referring now to FIG. 2, it will be apparent that parallelogram frame 50is generally cubically shaped and includes a second flex member 52'which is substantially a mirror image of flex member 52, and is alignedparallel with it. Although much of the discussion that follows isdirected to elements on flex member 52, e.g., flexures 32-42, it will beunderstood that flex member 52' includes substantially the sameelements. A base plate 60 (as shown in FIG. 8) extends through theinterior portion of parallelogram frame 50 between flex members 52 and52' and includes two grooves 102, adapted to engage mounting tabs 100.Mounting tabs 100 project inwardly from cross bar mounting tabs 54, andare secured to the base plate by means of two bolts (not shown).

With continued reference to FIG. 2, a driving mechanism 64 is providedto vibrate accelerometers 20 and 22 back and forth, in a directiontransverse to their sensitive axes. Driving mechanism 64 includes a coilframe 66 in which are mounted two electromagnetic coils 70. Coils 70 areheld in place by coil clamping bars 68, which are disposed on the topand bottom of coil frame 66, and are connected thereto with bolts 69. Amounting plate 72 extends outwardly from the center of coil frame 66 andincludes two mounting holes 74 for attachment to the supportingstructure of the body on which the Coriolis rate sensor is mounted.

The opposite surface of driving mechanism 64 is shown in FIG. 7, whereinit can be seen that mounting plate 72 is attached to a pivot plate 78 bymeans of a thin metal flexure 76. Pivot plate 78 is mounted within coilframe 66 so that both the pivot plate and the coil frame are free topivot about the bending axis of flexure 76 relative to mounting plate72. Electromagnetic coils 70 are each associated with a generally "C"shaped core 80, the ends of which include two core faces 82 that facetoward parallelogram frame 50. Core faces 82 are slightly beveled sothat their innermost edges extend outwardly slightly more than theiroutermost edges (as will be apparent from the exaggerated illustrationin FIGS. 3 and 6).

As shown in FIG. 2, two pole pieces 84 are mounted in a notch formedwithin parallelogram frame 50, and are each disposed proximate to thecore faces 82 of one of the electromagnetic coils 70. Each of polepieces 84 have a pole face 86, which is also slightly beveled so thatits innermost edge extends outwardly more than its outermost edge. Thesignificance of the beveled angle of core faces 82 and pole faces 86will be explained below.

Referring to FIG. 3, it can be seen that driving mechanism 64 isconnected to parallelogram frame 50 by a thin sheet metal link 88 (shownwith opposite ends broken away in FIGS. 2 and 7). One end of the link isattached to parallelogram frame 50 with a bolt 90, while the other endis fixedly attached to coil frame 66, e.g., by spot welding.Electromagnetic coils 70 are alternately energized with a sinusoidalcurrent provided by a power supply (not shown), creating an attractiveforce between first one and then the other of cores 80 and pole pieces84. The alternating magnetic attraction between cores 80 and pole pieces84 causes parallelogram frame 50 to vibrate, moving accelerometers 20and 22 laterally back and forth as indicated in FIG. 1. Link 88 forcescoil frame 66 and parallelogram frame 50 to pivot back and forth exactlyout of phase, although normally, the link is not required to transmitany force between the two frames unless the Coriolis rate sensor issubjected to an angular vibration about its rotation sensitive axis.

As will be apparent from FIG. 3, a plane 43 through the center ofmounting plate 72 and base plate 60 also passes through the center offlexures 40 and 42, dividing both the driving mechanism 64 and theparallelogram frame 50 vertically into two substantially symmetricalhalves. Front-to-back symmetry in driving mechanism 64 and parallelogramframe 50 is evident about a plane 92 shown in FIG. 4; this plane extendsthrough the center of percussion 46 of both accelerometers 20 and 22,bisecting parallelogram frame 50 and driving mechanism 64. Thus,relative to the views of FIGS. 3 and 4, parallelogram frame 50 anddriving mechanism 64 have both vertical and front-to-back symmetry. Theimportance of the symmetrical distribution of these structures will beevident in the discussion that follows.

Turning to FIG. 6, a cross sectional view of the parallelogram frame 50and driving mechanism 64 illustrates details of the accelerometers 20and 22 and shows the disposition of a linear variable differentialtransformer (LVDT) 106 which is mounted within a channel 104 of baseplate 60 (see FIG. 8). The LVDT 106 is cylindrical in shape, and issuitably attached to the upper portion of parallelogram frame 50 so thatit moves with accelerometer 20 as the parallelogram frame is vibratedfrom left to right. An LVDT core 108 extends through the center of LVDT106, is connected at each end to the lower portion of parallelogramframe 50, and moves with accelerometer 22 as it vibrates from left toright. The relative motion of LVDT core 108 and LVDT 106 thus producesan electrical signal proportional to the vibrational displacement ofaccelerometers 20 and 22 that is used by a servo control (not shown) tocontrol the sinusoidal electrical current energizing electromagneticcoils 70.

Accelerometer 20 includes a proof mass 20a suspended to pivot about aflexure 20b. One end of a crystal 19 is attached to the proof mass sothat acceleration along the sensitive axis changes the tension appliedto the crystal, modulating its resonant frequency. Accelerometer 22likewise includes a crystal 23 and a proof mass 22a, which pivots abouta flexure 22b. Counterweights 51 are provided for each proof mass 20aand 22a and are disposed inside the parallelogram frame 50, adjacent theaccelerometers on opposite sides of plane 58. FIG. 6 clearly shows howplane 58 connects the centers of percussion of the two accelerometers 20and 22, passing through their proof masses 20a and 22a.

Finally, with reference to FIG. 5, an end of parallelogram frame 50opposite that to which the vibrational driving force is applied bydriving mechanism 64 is shown to disclose the disposition of tuningstraps 110. Tuning straps 110 are relatively thin metal strips which areconnected by bolts 112 between the accelerometer support surfaces 24 and26 and base plate 60, and are used to off-set the stiffness of flexure40 as will be apparent from the discussion that follows below.

OPERATIONAL ADVANTAGES OF THE INVENTION

The design of parallelogram frame 50 is intended to avoid errors in theoutput signal produced by accelerometers 20 and 22 that may result fromvibration in a direction aligned with their sensitive axes. Flexures 34and 38 are oriented so that their "long" axis lies in plane 58, parallelwith a line connecting the centers of percussion of accelerometers 20and 22. The flexures are extremely stiff along their long axis (having acompression yield strength greater than 200,000 lbs./sq. inch), thusproviding a substantially solid metal path connecting the accelerometersbetween their centers of percussion. Any vibration directed in alignmentwith plane 58 and with the sensitive axis is applied equally to theaccelerometers through the linkage member 30 because of the orientationof flexures 34 and 38, so that both accelerometers 20 and 22 experiencethe same common mode input. As a result, common mode vibration cancelsin the Coriolis rate channel. In addition, the stiffness presented byflexures 34 and 38 aligned as shown in FIG. 3 raises the naturalfrequency of parallelogram frame 50 to a relatively high value, e.g.,six kiloHertz or higher. Because flexures 34 and 38 are commonly alignedon a plane with the centers of gravity of each accelerometer and itsassociated mass and the centers of percussion of the accelerometers 20and 22, vibrations directed in alignment with the sensitive axes of theaccelerometers will not produce a torque that might tend to producefalse angular rate errors in the accelerometer output signals, and willnot promote a resonant response in the parallelogram frame 50.

Flexures 32 and 36 are oriented so that their relatively stiff long axesdirectly transmit the driving force provided by drive mechanism 64 intothe centers of gravity of the combined mass of the accelerometers andtheir mounting surfaces, and the force centers of the driving forceproviding by each core 80 and pole piece 84 pair is generally alignedwith these flexures. The location of the centers of gravity of theaccelerometers 20 and 22 and their mounting surfaces 24 and 26 isadjusted by adding an appropriate counter weight 44 on each electronicpackage 21 and 25 and appropriate counterweights 51 inside theparallelogram frame 50, so that the center of gravity of eachaccelerometer and its associated mass lies in alignment with one offlexures 32 and 36. Alignment of the centers of gravity with the forcecenter through flexures 32 and 36 reduces excitation of parallelogramframe 50 by eliminating extraneous cross axial force (other than theforce provided by driving mechanism 64 to dither accelerometers 20 and22).

The shape and size of linkage member 30 was selected to provide the samemass balance as linkage member 28. Using a reiterative computeralgorithm, the shape of linkage member 30 was successively adjusted sothat the product of the distance between the bending axis of flexure 42and each mass element of linkage member 30, when integrated, resulted ina moment equal to the moment of linkage member 28 computed in a similarfashion. Consequently, parallelogram frame 50 is balanced with respectto vibrations directed in alignment with the sensitive axis. The torqueon linkage members 28 and 30 arising from application of a vibrationalforce acting in a direction aligned with the sensitive axes of theaccelerometers is matched and therefore cancels.

As previously mentioned, the parallelogram frame 50 and driver mechanism64 are symmetrical in mass and shape about a plane 43 extending(horizontally as shown in FIG. 3) through base plate 60. As a result,the Coriolis rate sensor is insensitive to extraneous linear vibrationdirected in alignment with plane 43 (other than the dither vibration).

As noted with respect to plane 92 shown in FIG. 4, both the drivingmechanism 64 and parallelogram frame 50 are symmetrical in mass andshape, and this front-to-back symmetry coupled with the verticalsymmetry just described inherently dynamically balances the Coriolisrate sensor, preventing the driving force provided by driving mechanism64 or any other external force applied in alignment therewith fromproducing a torque due to imbalance that would otherwise tend to causethe parallelogram frame 50 to roll.

The moment of inertia of driving mechanism 64 is adjusted to equal themoment of inertia of the parallelogram frame 50 with attachedaccelerometers 20 and 22, by trimming the weight of coil clamping bars68. Since the coil frame 66 and parallelogram frame 50 rock back andforth exactly out of phase, driving mechanism 64 does not produce anynet reaction into base plate 60, mounting plate 72, or into thesupporting structure to which they are attached.

Driving mechanism 64 and parallelogram frame 50 are also insensitive toangular vibrations. Partly, this is due to their symmetry about thehorizontal and vertical axes, i.e., about planes 43 and 92, and partlybecause they are trimmed to have equal moments of inertia. In addition,link 88, which extends between coil frame 66 and parallelogram frame 50insures that any angular torque acting on either the coil frame 66 orthe parallelogram frame 50 is transmitted through the link to the otherframe. Therefore, the back and forth vibration motion of theparallelogram frame 50 and the driving mechanism 64 remains unaffectedby base angular vibration of the Coriolis rate sensor about its rotationsensitive axis, (the X axis in FIG. 1).

Referring back to FIG. 1, it will be apparent that as the parallelogramframe flexes under the driving force provided by driving mechanism 64,the accelerometer supporting surfaces 24 and 26 on which accelerometers20 and 22 are mounted tend to tilt slightly or to rotate about theangular rate axis, X, due to cross axis compliance in the flexures 32,34, 36, 38, 40 and 42. Since the Coriolis rate sensor uses linearaccelerometers, the tilt experienced by accelerometers 20 and 22 dependsupon the location of the center of rotation. However, by controlling thecenter of rotation of the accelerometers so that it is coaligned withthe line connecting the accelerometers' centers of percussion, a simplebalance condition pertains.

A much simplified model representing a force balance condition asapplied to the rotation of one of the accelerometers is represented inFIG. 9. As shown therein, the center of rotation is made coincident withthe center of percussion 46 of the accelerometer so that only two forcesare active to rotate the accelerometer mounting surface--the cross axiscompliance of flexure 40, K_(c), and an added tuning force, K_(s). Theforce K_(s) is adjusted so that the product K_(s) times D₁ equals theproduct K_(c) times D₂, where D₂ equals the distance between the centerof rotation and flexure 32 (or 36), and D₁ equals a distance between thecenter of rotation and the point at which a force K_(s) is applied toaccelerometer mounting surface 24 (or 26). By making the two productsequal, the contribution of a force K_(v), which is equal to the crossaxis stiffness of flexure 42, is eliminated from the equation. The forceK_(s) is provided by connecting four tuning straps 110 between theaccelerometer support surfaces 24 and 26 and base 60, having therequired stiffness, K_(s), to produce the "force times distance"equality described above. When this condition is achieved,accelerometers 20 and 22 sense only a very small common mode centrifugalforce at twice the dither frequency, which cancels during the processingof the angular rate signal.

Driving mechanism 64 provides an electromagnetic attraction betweencores 80 and pole pieces 84. This force is proportional to the square ofthe reciprocal of the distance between the core face 82 and pole face86. As shown in a greatly exaggerated fashion in FIG. 10, both core face82 and pole face 86 are beveled at an angle α. When electromagneticcoils 70 are energized, an attractive force is generated between forcecenters 114 along a line, L, causing coil frame 66 to pivot aboutflexure 76 and parallelogram frame 50 to pivot about flexures 32 through42, and in particular, flexure 40. Force center 114 within core 80 islocated at a radius R_(m) from flexure 76, while force center 114 withinpole piece 84 is located at a radius R_(p) from flexure 40. As core face82 and pole face 86 rock toward each other, they tilt and dip down. Byproperly selecting the tilt angle α, force centers 114 are maintained atthe junction of L and R. If the core face and pole face were notbeveled, the center of force would be raised as the two faces rockedtoward each other, because the gap between the core and pole faces wouldbe smaller near the top than at the bottom. This effect is offset bybeveling the faces at the angle α so that the change in force centerthat would occur due to the dipping of the core and pole piece is justoffset by the change resulting from the beveled faces. To maintain theforce center between core 80 and pole piece 84 in alignment with theflexures 32 and 36, the core 80 and pole piece 86 are shifted by thedistance d, thereby offsetting the change in the position of the forcecenters resulting from beveling the core and pole piece faces 82 and 84,at the angle α. As a result, the force centers 114 are always maintainedin alignment with flexures 32 and 36.

While the present invention has been disclosed with respect to apreferred embodiment and modifications thereto, further modificationswill be apparent to those of ordinary skill in the art within the scopeof the claims that follow. It is not intended that the invention belimited by the disclosure, but instead that its scope be determinedentirely by reference to the claims which follow hereinbelow.

The embodiments of the invention in which an exlusive property orprivilege is claimed are defined as follows:
 1. A frame for use in aCoriolis rate sensor including two accelerometers each having apreferred axis, comprising:two accelerometer carriers disposed onopposite sides of the frame and adapted for mounting the twoaccelerometers with their preferred axes in alignment; two substantiallyparallel flex members, each extending between the two accelerometercarriers at opposite sides thereof, the flex members each including across brace disposed at their center, adapted for attaching the frame toa supporting structure, and further including a plurality of flexureshaving parallel bending axes, the flexures being disposed at the cornersof a parallelogram, with one of the flexures connecting two sides of theparallelogram at each corner and one of the flexures disposed at eachend of the cross brace and connecting the centers of two sides of theparallelogram, the flexures at each end of one of said two sides of eachflex member being oriented to provide maximum stiffness on a linebetween the two carriers and disposed so that when the twoaccelerometers are mounted on the carriers, the centers of mass of eachcarrier and the accelerometer mounted thereon are aligned with theflexures at each end of said one side.
 2. The frame of claim 1 whereinfor each flex member, the moment of said one side of the flex memberabout the bending axis of the flexure connecting the cross brace to saidone side equals the moment of the other of said two sides of the flexmember about the bending axis of the flexure connecting the cross braceto said other side, thereby preventing a rotational torque being appliedto the frame as a result of a vibrational component directed parallel tothe preferred axes of the accelerometers.
 3. The frame of claim 1further comprising a base plate disposed in the center of the frame andconnected to a center portion of each of the cross braces, one end ofthe base plate being adapted to attach to the supporting structure. 4.The frame of claim 3 wherein the center of the base plate defines acentral plane through the frame that is intermediate both carriers, andwherein the frame is substantially symmetrical in both shape and massabout said plane, preventing a rotational torque from being applied tothe frame as a result of a vibrational component directed transverselyto the preferred axes and parallel to the bending axes of the flexures.5. The frame of claim 3 further comprising at least one tuning strapconnecting the accelerometer carriers to the base plate, and selected tohave a stiffness balancing a cross axis compliance associated with theflexures.
 6. The frame of claim 1 wherein the frame is substantiallysymmetrical in both shape and mass about a plane that is equidistantfrom and intermediate the flex member, providing a dynamic balance. 7.The frame of claim 1 further comprising means adapted for magneticallyand mechanically coupling the flex members to a driving mechanismoperative to vibrate the accelerometers back and forth.
 8. A frame foruse in a Coriolis rate sensor having two accelerometers mounted withtheir preferred axes in alignment, comprising:(a) two accelerometermounting pads disposed on opposite sides of the frame, each beingadapted to mount one of the accelerometers so that their preferred axesare aligned; (b) parallelogram means for linking the accelerometermounting pads in parallel alignment and including a plurality offlexures enabling the accelerometer mounting pads and accelerometersmounted thereon to vibrate back and forth in a direction transverse totheir preferred axes; (c) attachment means for attaching a centralportion of the frame to a supporting structure, the attachment meansbeing pivotably connected to the parallelogram means by the plurality offlexures; and (d) common mode connection means for rigidly connectingthe two accelerometer mounting pads along a path that is aligned with aline extending through a center of percussion associated with eachaccelerometer, the common mode connection means comprising a portion ofthe parallelogram means and including a plurality of flexures orientedin alignment with said path and differently than other of the flexuresof the parallelogram means, the orientation insuring that bothaccelerometers are subjected to the same motion directed along theirpreferred axes.
 9. The frame of claim 8 wherein the center of percussionassociated with each accelerometer is coincident with a center ofgravity associated with each mounting pad and accelerometer, and whereinthe centers of gravity of the accelerometers are rigidly connected bythe common mode connection means along said path.
 10. The frame of claim8 wherein the attachment means comprise a base plate connected to thesupporting structure at one end and to a central portion of theparallelogram means adjacent the other end.
 11. The frame of claim 8wherein the frame is symmetrical both in shape and mass about twoorthogonal planes extending through the center of the frame, one ofwhich is aligned with the preferred axes of the accelerometers.
 12. Theframe of claim 11 wherein the parallelogram means are dynamicallybalanced.
 13. The frame of claim 8 further comprising means forcompensating a cross axis compliance associated with the flexures toeliminate an error signal resulting from a non-common mode rotationaltilting of the accelerometers that would otherwise be produced when theaccelerometers vibrate back and forth.
 14. A frame for use in a Coriolisrate sensor including two accelerometers each having a preferred axis,comprising:two accelerometer carriers disposed on opposite sides of theframe and adapted for mounting the two accelerometers with theirpreferred axes in alignment; two substantially parallel flex members,each extending between the two accelerometer carriers at opposite sidesthereof, the flex members each including a cross brace disposed at theircenter, adapted for attaching the frame to a supporting structure, and aplurality of flexures having parallel bending axes, the flexures beingdisposed so as to define a parallelogram, by connecting the sides of theparallelogram at each of the corners of the parallelogram and connectingthe cross brace to the centers of two of the sides of the parallelogramthat extend transversely between the accelerometer carriers, one of saidtwo sides of the parallelogram including flexures at each end that areoriented to provide maximum stiffness on a line between the two carriersand disposed so that when the two accelerometers are mounted on thecarriers, the centers of mass of each carrier and the accelerometermounted thereon, and a center of percussion associated with eachaccelerometer, are aligned with the flexures at each end of said oneside.